EVAP system leak causes car to shut off only when shifting out of park?

So it all starts with the drive. Going downhill my car seems to shift way too low causing a spike in the revving once I slowly step on the brake to slow down. And sometimes difficult to put into proper gear I need to shift to neutral then back onto drive just to balance it. Now that's 1 problem. Second is, I have a evap system leak. Gas cap is new and that's all I changed. Haven't touched or check the 2 valves. But my car seems to die out sometimes when I go for a long drive no problem then suddenly when I try to shift out of park or reverse going into drive or neutral my car dies out completely with battery caution light on. But when I start back up again it runs perfectly until I'm about to drive off, when I shift once more out of park, vehicle shuts off again. I'm not sure what causes it to shut off if the evap system leak has a role in this process but I'm worried for future problems. Please help.